What is the general solution for 1+2sin^2(x)-3sin(x)=0 ?

The general solution for 1+2sin^2(x)-3sin(x)=0 is x= pi/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin

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1+2sin^2(x)-3sin(x)=0

1 + 2 sin^{2} (x) - 3 sin (x) = 0

x = \frac{π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

1 + 2 sin^{2} (x) - 3 sin (x) = 0

Solve by substitution

sin (x) = 1, sin (x) = \frac{1}{2}

sin (x) = 1 : x = \frac{π}{2} + 2 πn

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

4 tan^{2} (x) = - 3 tan (x) + tan^{2} (x)

\frac{1}{2} = \frac{1}{2} \cdot cos (4.2 t + \frac{π}{6})

120 = 8 3^{2} + 7 5^{2} - 2 \cdot 83 \cdot 75 \cdot cos (x)

cos (u) = \frac{7}{25}

sin (x) + cos (x) = 1, 0 \leq x < 2 π

What is the general solution for 1+2sin^2(x)-3sin(x)=0 ?
The general solution for 1+2sin^2(x)-3sin(x)=0 is x= pi/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin